Research On Synchronization Of Complex Dynamical Networks Via Pinning Control Protocol

Complex dynamical network is a non-trivial topological network,which contains a large number of interacting nodes or individual systems with nonlinear dynamics.Synchronization is a typical collective behavior of complex dynamical networks and has gained particular research interests in the past few years.In some cases where a complex network cannot achieve spontaneous synchronization through their own dynamic evolutionary process and the mutual interaction among the connected nodes,control strategies play an essential role in compelling the network to reach consensus or driving the network to accomplish the assigned collaborative tasks.In particular,pinning control is a feedback control strategy for synchronization by selectively applying control actions to a small fraction of network nodes.Despite relatively fruitful results on synchronization control issues,there are still some weakness and problems that need to be addressed,for example,the lack of theoretical models that are closer to real-world complex networks,the stringent requirements on network topologies,the network-induced time delays and data packet dropouts due to network traffic congestion,the shared transmission medium and the open network environment that are vulnerable to malicious attackers,and the increased demand for more reasonable and effective synchronization control strategies and so forth.To solve the above-mentioned problems,the issue of synchronization in complex dynamical networks via a pining control strategy is investigated in the thesis with a careful and comprehensive consideration of the following factors:system modeling approaches,network topologies,non-ideal communication environment,synchronization control strategies,performance requirements,stability analysis methods,etc.The aim is to design synchronization controllers and establish synchronization criteria for complex dynamical networks under non-ideal communication networks.In view of the commonality of the leader-follower consensus problem of multi-agent systems and the pinning synchronization problem of complex dynamical networks,the proposed techniques and the obtained results for complex dynamical networks are extended to multi-agent systems.More specifically,the main contributions of the thesis are summarized as follows:(1)Provide a solotion for the global pinning synchronization problem of complex dynamical networks based on pinning control and adaptive techniques.For a network with a directed and weighted topology,a pinning control strategy is utilized,where only a limited number of nodes(called pinned nodes)is directly steered by an external leader(called pinner)whose control actions are exerted onto the pinned nodes and propagated to the rest nodes through communication and interaction so as to bring the entire network to follow the pinner's reference trajectory.Under the framework of a modeling approach based on the augmented Laplacian matrix formed by original nodes and the pinner,and a analysis method originated from the sub-matrix of the Laplacian matrix corresponding to unpinned nodes,a SCC(strongly connected component)-based pinning strategy and a degree-difference-based pinning strategy are proposed,respectively.By using Lyapunov stability theory,sufficient conditions to guarantee global pinning synchronization of the network are then derived.It should be noted that theoretical values of the coupling strength and pinning control gains are too conservative and the calculation of pinning control gains depends on the global topology.Taking these issues into account,an adaptive strategy is devised to perform on-line parameter adjustment and generate optimal solutions for the coupling strength and pinning control gains.By using Lyapunov stability theory,sufficient conditions for the global adaptive pinning synchronization of the network are established.(2)Provide a solution for the global mean-square pinning synchronization problem of complex dynamical networks based on stochastic pinning control.The investigated network has a directed and weighted topology and is subject to network-induced constraints,including mixed time delays,hybrid couplings,random data packet dropouts and multiple stochastic disturbances.The mixed delays involve the internal delay happened inside the individual system and the discrete delay and the distributed delay caused by network imperfections and constraints.The hybrid couplings are portrayed in two forms:non-delayed couplings and delayed couplings.The phenomenon of random packet losses is described as a binary random variable which obeys the Bernoulli distribution taking values of 0 and 1 with a certain probability.The multiple noisy processes are characterized by Brownian motions,which act on all coupling terms as well as the overall dynamics equation.For such a complex network,a randomly occurring pinning control strategy is developed.By applying the Lyapunov stability theory and stochastic analysis techniques,mean-square pinning synchronization conditions and a controller design scheme are then given.(3)Solve the issue of global robust H_?pinning synchronization for complex dynamical networks via an event-triggered mechanism.The network is subject to transmission delays,parametric uncertainties and external disturbances.A directed and weighted communication topology is taken into account,and the phenomenon of uncertainties is reflected in both modeling and inner coupling matrices.In order to avoid unnecessary information interaction among nodes and reduce the transmission pressure,an event-triggered communication mechanism with an asynchronous sampling manner is proposed,with which the Zeno behaviour can be absolutely avoided.Under this scheme,an event-driven pinning control protocol is designed to reduce the frequency of controller updates and the computational burden.By the Lyapunov-Krasovskii functional approach,input delay method,Jensen inequality and free-weighting matrix approach,sufficient conditions are deduced to guarantee that both global robust pinning synchronization and a desired H_?performance are achieved for the concerned network.(4)Solve the issue of leader-follower consensus for multi-agent systems via a resilient event-triggered mechanism.Consider a multi-agent system with transmission delays and denial-of-service(Do S)attacks.In order to avoid redundancy and excessive information exchange among agents and allow the system to tolerate adverse effects of malicious attacks,a resilient event-triggered mechanism is proposed,where the event-triggered condition is constructed based on hybrid relative state errors.Under the presented mechanism,an event-driven tracking control protocol is formed to ensure leader-following consensus and save computational resources.Then,by constructing a new Lyapunov-Krasovskii functional,less conservative results and a new version of consensus criteria are derived,the maximum Do S attack duration is provided,and meanwhile a joint design scheme is delivered to obtain the control gain in the event-driven consensus control strategy and the weight matrix in the resilient event-triggered mechanism simultaneously.